Abstract
The heart of Schoof's algorithm for computing the cardinality m of an elliptic curve over a finite field is the computation of m modulo small primes l. Elkies and Atkin have designed practical improvements to the basic algorithm, that make use of “good” primes l. We show how to use powers of good primes in an efficient way. This is done by computing isogenies between curves over the ground field. A new structure appears, called “isogeny cycle”. We investigate some properties of this structure.
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References
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© 1994 Springer-Verlag Berlin Heidelberg
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Couveignes, JM., Morain, F. (1994). Schoof's algorithm and isogeny cycles. In: Adleman, L.M., Huang, MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58691-1_42
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DOI: https://doi.org/10.1007/3-540-58691-1_42
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